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ExamsProbability Questions
FACTS AND FORMULAE FOR PROBABILITY QUESTIONS
1. Experiment : An operation which can produce some well-defined outcomes is called an experiment.
2. Random Experiment :An experiment in which all possible outcomes are know and the exact output cannot be predicted in advance, is called a random experiment.
Ex :
i. Tossing a fair coin.
ii. Rolling an unbiased dice.
iii. Drawing a card from a pack of well-shuffled cards.
3. Details of above experiments:
i. When we throw a coin, then either a Head (H) or a Tail (T) appears.
ii. A dice is a solid cube, having 6 faces, marked 1, 2, 3, 4, 5, 6 respectively. When we throw a die, the outcome is the number that appears on its upper face.
iii. A pack of cards has 52 cards.
- It has 13 cards of each suit, name Spades, Clubs, Hearts and Diamonds.
- Cards of spades and clubs are black cards.
- Cards of hearts and diamonds are red cards.
There are 4 honours of each unit. There are Kings, Queens and Jacks. These are all called face cards.
4. Sample Space: When we perform an experiment, then the set S of all possible outcomes is called the sample space.
Ex :
1. In tossing a coin, S = {H, T}
2. If two coins are tossed, the S = {HH, HT, TH, TT}.
3. In rolling a dice, we have, S = {1, 2, 3, 4, 5, 6}.
Event : Any subset of a sample space is called an event.
5. Probability of Occurrence of an Event :
Let S be the sample and let E be an event.
Then,
6. Results on Probability :
i. P(S) = 1 ii. iii.
iv. For any events A and B we have :
v. If denotes (not-A), then